Spherical polyelectrolyte brushes: Comparison between annealed and quenched brushes

We report on a study of spherical polyelectrolyte brushes that consist of a solid core onto which linear polyelectrolyte chains are chemically grafted. The core particles are made up of solid poly(styrene) and have a radius R of ca. 50 nm. As polyelectrolyte chains the weak polyelectrolyte poly(acrylic acid) or the strong polyelectrolyte poly (styrenesulfonate) was used. These chains were generated directly on the surface of the core particles by a grafting-from technique. Hence, the chains are chemically bound to the surface but can be cleaved off and analyzed separately. The contour length L-c and the number of grafted chains per unit area sigma can thus be determined accurately. The thickness L of the brush layer on the surface has been determined by dynamic light scattering. It is measured for different L-c/R as a function of pH, ionic strength, and valency of counterions. Annealed brushes exhibit a transition with increasing pH in which the chains are stretched to nearly full length. This can be traced back to the building up of the osmotic pressure of the counterions. The brush height L decreases considerably with increasing ionic strength, most notably when adding divalent ions. The entire set of L as a function of R, L-c, and sigma can be fully explained in terms of a simple two-parameter theory developed by Hariharan et al. [Macromolecules 31, 7514 (1998)].